Predict the hybridization and the nature of complex in [MnCl6]3−.

The correct answer is Option (3) → sp³d², high spin complex

By valence bond theory, an octahedral complex uses six hybrid orbitals. If two inner (n−1)d orbitals are free, the hybridisation is d²sp³ (inner orbital, low spin). If the electrons stay unpaired and no inner d orbitals are free, the outer nd orbitals are used and the hybridisation is sp³d² (outer orbital, high spin). Whether the electrons pair up depends on the ligand: strong field ligands (\( \ce{CN^{-}} \), CO) force pairing, weak field ligands (\( \ce{Cl^{-}} \), \( \ce{F^{-}} \), \( \ce{H2O} \)) do not.

In \( \ce{[MnCl6]^{3-}} \), the oxidation state of Mn is x + 6(−1) = −3, so x = +3.

    \( \displaystyle \ce{Mn}\ (Z=25):\ [\ce{Ar}]\,3d^5\,4s^2 \)

    \( \displaystyle \ce{Mn^3+}:\ [\ce{Ar}]\,3d^4 \)

\( \ce{Cl^{-}} \) is a weak field ligand, so the four 3d electrons remain unpaired and occupy four of the five 3d orbitals. Two empty 3d orbitals are not available, so \( \ce{Mn^{3+}} \) uses one 4s, three 4p and two 4d orbitals. The complex is sp³d², outer orbital, with four unpaired electrons, that is a high spin complex.

Why the other options are incorrect

• Option (1) sp³d², low spin complex — Incorrect. Outer orbital (sp³d²) complexes form only when the electrons are not paired, so they are always high spin.

• Option (2) d²sp³, low spin complex — Incorrect. This is correct for \( \ce{[Mn(CN)6]^{3-}} \), where the strong field \( \ce{CN^{-}} \) ligand pairs the electrons and frees two 3d orbitals; \( \ce{Cl^{-}} \) cannot do this.

• Option (4) d²sp³, high spin complex — Incorrect. Using two inner d orbitals requires pairing of the d electrons, so a d²sp³ complex of a d⁴ ion cannot be high spin.

NCERT (2026-27 edition):
Valence Bond Theory – “… In the formation of this complex, since the inner d orbital (3d) is used in hybridisation, the complex, [Co(NH₃)₆]³⁺ is called an inner orbital or low spin or spin paired complex. The paramagnetic octahedral complex, [CoF₆]^3– uses outer orbital (4d) in hybridisation (sp³d²). It is thus called outer orbital or high spin or spin free complex.”